Unless you specify the
SPLINE option, the G3GRID procedure is an interpolation procedure.
It calculates the
z values
for
x,
y points that are missing from the input data set. The surface that
is formed by the interpolated data passes precisely through the data
points in the input data set.
This method of interpolation
works best for fairly smooth functions, with values given at uniformly
distributed points in the plane. If the data points in the input data
set are erratic, the default interpolated surface can be erratic.
This default method
is a modification of that described by Akima (1978). This method consists
of the following actions:
-
dividing the plane into
non-overlapping triangles that use the positions of the available
points
-
fitting a bivariate
fifth degree polynomial within each triangle
-
calculating the interpolated
values by evaluating the polynomial at each grid point that falls
in the triangle
The coefficients for
the polynomial are computed based on the following criteria:
-
the values of the function at the
vertices of the triangle
-
the estimated values for the first,
and second derivatives of the function at the vertices
The estimates of the
first, and second derivatives are computed using the
n nearest neighbors of the point, where
n is the number specified in the GRID statement's
NEAR= option. A Delauney triangulation (Ripley 1981, p. 38), is used
for the default method. The coordinates of the triangles are available
in an output data set, if requested by the OUTTRI= option, in the
PROC G3GRID statement. This is the default interpolation method.